Positronium formation in a laser field including the dressing effect

A detailed analysis is given for the study of positronium (Ps) formation in $e^{+}$+H collisions in the presence of a homogeneous, single-mode laser field, considering full interaction. The projectile–laser-field interaction and the dressing effect on the target hydrogen atom and the Ps atom in the final channel are considered to first order. The field is treated classically in the dipole approximation to calculate the dressing effect. We consider the dressing effects of the hydrogen atom and the Ps atom for the field directions both parallel and perpendicular to the incident momentum (scr${\mathrm{E}}_0$∥${\mathrm{k}}_i$ and scr${\mathrm{E}}_0$⊥${\mathrm{k}}_i$). The dressing effects are shown to produce significant modifications of the differential cross section. The differential cross sections for Ps formation with and without the dressing are presented for no-photon and one-photon (l=0,±1) exchange at 50, 75, 100, and 200 eV energies with laser-field amplitude ‖scr${\mathrm{E}}_0$‖=0.02 a.u. and the angular frequency ω=0.074 a.u.